Advertisement

General Relativity and Gravitation

, Volume 41, Issue 4, pp 903–917 | Cite as

Black holes, AdS, and CFTs

  • Donald MarolfEmail author
Open Access
Research Article

Abstract

This brief conference proceeding attempts to explain the implications of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence for black hole entropy in a language accessible to relativists and other non-string theorists. The main conclusion is that the Bekenstein–Hawking entropy S BH is the density of states associated with certain superselections sectors, defined by what may be called the algebra of boundary observables. Interestingly while there is a valid context in which this result can be restated as “S BH counts all states inside the black hole,” there may also be another in which it may be restated as “S BH does not count all states inside the black hole, but only those that are distinguishable from the outside.” The arguments and conclusions represent the author’s translation of the community’s collective wisdom, combined with a few recent results.

Keywords

Black hole entropy AdS/CFT 

Notes

Acknowledgments

This work was supported in part by the US National Science Foundation under Grant No. PHY05-55669, and by funds from the University of California.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. Wheeler, J.A.: In: DeWitt, B.S., DeWitt, C.M. (eds.) Relativity, Groups, and Fields. Gordon and Breach, New York (1964)Google Scholar
  2. Maldacena, J.M.: The large N limit of superconformal field theories and supergravity. Adv. Theor. Math. Phys. 2, 231 (1998) [Int. J. Theor. Phys. 38, 1113 (1999)][arXiv:hep-th/9711200]Google Scholar
  3. Hsu, S.D.H., Reeb, D.: Unitarity and the Hilbert space of quantum gravity. arXiv:0803.4212 [hep-th]Google Scholar
  4. Henningson, M., Skenderis, K.: The holographic Weyl anomaly. JHEP 9807, 023 (1998) [arXiv:hep-th/9806087]Google Scholar
  5. Balasubramanian V., Kraus P.: A stress tensor for anti-de Sitter gravity. Commun. Math. Phys. 208, 413 (1999) [arXiv:hep-th/9902121]zbMATHCrossRefMathSciNetGoogle Scholar
  6. Fefferman, C., Graham, C.R.: Conformal Invariants. In: Elie Cartan et les Mathématiques d’aujourd’hui. (Astérisque, 1985) 95Google Scholar
  7. Hollands S., Ishibashi A., Marolf D.: Comparison between various notions of conserved charges in asymptotically AdS-spacetimes. Class. Quant. Gravit. 22, 2881 (2005) [arXiv:hep-th/0503045]zbMATHCrossRefADSMathSciNetGoogle Scholar
  8. Hollands S., Ishibashi A., Marolf D.: Counter-term charges generate bulk symmetries. Phys. Rev. D 72, 104025 (2005) [arXiv:hep-th/0503105]CrossRefADSMathSciNetGoogle Scholar
  9. Ashtekar A., Magnon A.: Asymptotically anti-de Sitter space-times. Classical Quantum Gravit. Lett. 1, L39 (1984)CrossRefADSMathSciNetGoogle Scholar
  10. Ashtekar A., Das S.: Asymptotically anti-de Sitter space-times: conserved quantities. Class. Quant. Gravit. 17, L17 (2000) [arXiv:hep-th/9911230]zbMATHCrossRefMathSciNetGoogle Scholar
  11. Iyer V., Wald R.M.: Some properties of Noether charge and a proposal for dynamical black hole entropy. Phys. Rev. D 50, 846 (1994) [arXiv:gr-qc/9403028]CrossRefADSMathSciNetGoogle Scholar
  12. Wald R.M., Zoupas A.: A general definition of “Conserved Quantities” in general relativity and other theories of gravity. Phys. Rev. D 61, 084027 (2000) [arXiv:gr-qc/9911095]CrossRefADSMathSciNetGoogle Scholar
  13. Papadimitriou I., Skenderis K.: Thermodynamics of asymptotically locally AdS spacetimes. JHEP 0508, 004 (2005) [arXiv:hep-th/0505190]CrossRefADSMathSciNetGoogle Scholar
  14. Maldacena J.M.: Wilson loops in large N field theories. Phys. Rev. Lett. 80, 4859 (1998) [arXiv:hep-th/9803002]zbMATHCrossRefMathSciNetGoogle Scholar
  15. Rehren K.H.: Local quantum observables in the Anti-deSitter—conformal QFT correspondence. Phys. Lett. B 493, 383 (2000) [arXiv:hep-th/0003120]CrossRefADSMathSciNetGoogle Scholar
  16. Giddings S.B.: The boundary S-matrix and the AdS to CFT dictionary. Phys. Rev. Lett. 83, 2707 (1999) [arXiv:hep-th/9903048]zbMATHCrossRefADSMathSciNetGoogle Scholar
  17. Witten E.: Anti-de Sitter space and holography. Adv. Theor. Math. Phys. 2, 253 (1998) [arXiv:hep-th/9802150]zbMATHMathSciNetGoogle Scholar
  18. Schwinger J.S.: On the green’s functions of quantized fields. 1. Proc. Nat. Acad. Sci. 37, 452 (1951)CrossRefADSMathSciNetGoogle Scholar
  19. DeWitt B.S.: Dynamical Theory of Groups and Fields. Gordon and Breach, New York (1965)zbMATHGoogle Scholar
  20. DeWitt, B.S.: In: DeWitt, B.S., Stora, R. (eds.) Relativity, Groups, and Topology II: Les Houches 1983. North-Holland, Amsterdam (1984)Google Scholar
  21. DeWitt B.S.: The Global Approach to Quantum Field Theory. Oxford University Press, New York (2003)zbMATHGoogle Scholar
  22. Marolf D.: States and boundary terms: subtleties of lorentzian AdS/CFT. JHEP 0505, 042 (2005) [arXiv:hep-th/0412032]CrossRefADSMathSciNetGoogle Scholar
  23. Freivogel B., Hubeny V.E., Maloney A., Myers R.C., Rangamani M., Shenker S.: Inflation in AdS/CFT. JHEP 0603, 007 (2006) [arXiv:hep-th/0510046]CrossRefADSMathSciNetGoogle Scholar
  24. Marolf, D.: Unitarity and Holography in Gravitational Physics. arXiv:0808.2842 [gr-qc]Google Scholar
  25. Marolf, D.: Holographic Thought Experiments. arXiv:0808.2845 [gr-qc]Google Scholar
  26. Wootters W.K., Zurek W.H.: A single quantum cannot be cloned. Nature 299, 802 (1982)CrossRefADSGoogle Scholar
  27. Dieks D.: Communication By Epr Devices. Phys. Lett. A 92, 271 (1982)CrossRefADSGoogle Scholar
  28. Jacobson, T.: On the nature of black hole entropy. In: Burgess, C.P., Myers, R. (eds.) General Relativity and Relativistic Astrophysics, Eighth Canadian Conference, Montréal, Québec. AIP, Melville (1999). [arXiv:gr-qc/9908031]Google Scholar
  29. Coleman S.R.: Black holes as red herrings: topological fluctuations and the loss of quantum coherence. Nucl. Phys. B 307, 867 (1988)CrossRefADSGoogle Scholar
  30. Klebanov I.R., Susskind L., Banks T.: Wormholes and the cosmological constant. Nucl. Phys. B 317, 665 (1989)CrossRefADSMathSciNetGoogle Scholar
  31. Preskill J.: Wormholes in space-time and the constants of nature. Nucl. Phys. B 323, 141 (1989)CrossRefADSMathSciNetGoogle Scholar
  32. Maldacena J.M.: Eternal black holes in Anti-de-Sitter. JHEP 0304, 021 (2003) [arXiv:hep-th/0106112]CrossRefADSMathSciNetGoogle Scholar
  33. Festuccia G., Liu H.: The arrow of time, black holes, and quantum mixing of large N Yang-Mills theories. JHEP 0712, 027 (2007) [arXiv:hep-th/0611098]CrossRefADSMathSciNetGoogle Scholar
  34. Iizuka N., Kabat D.N., Lifschytz G., Lowe D.A.: Probing black holes in non-perturbative gauge theory. Phys. Rev. D 65, 024012 (2002) [arXiv:hep-th/0108006]CrossRefADSMathSciNetGoogle Scholar
  35. Iizuka, N., Polchinski, J.: A Matrix Model for Black Hole Thermalization. arXiv:0801.3657 [hep-th]Google Scholar
  36. Iizuka, N., Okuda, T., Polchinski, J.: Matrix Models for the Black Hole Information Paradox. arXiv:0808.0530 [hep-th]Google Scholar
  37. Cardy J.L.: Operator content of two-dimensional conformally invariant theories. Nucl. Phys. B 270, 186 (1986)zbMATHCrossRefADSMathSciNetGoogle Scholar
  38. Strominger A.: Black hole entropy from near-horizon microstates JHEP 9802, 009 (1998) [arXiv:hep-th/9712251]MathSciNetGoogle Scholar
  39. Freivogel B., Hubeny V.E., Maloney A., Myers R.C., Rangamani M., Shenker S.: Inflation in AdS/CFT. JHEP 0603, 007 (2006) [arXiv:hep-th/0510046]CrossRefADSMathSciNetGoogle Scholar
  40. Farhi E., Guth A.H., Guven J.: Is it possible to create a universe in the laboratory by quantum tunneling. Nucl. Phys. B 339, 417 (1990)CrossRefADSMathSciNetGoogle Scholar
  41. Fischler W., Morgan D., Polchinski J.: Quantum nucleation of false vacuum bubbles. Phys. Rev. D 41, 2638 (1990)CrossRefADSMathSciNetGoogle Scholar
  42. Fischler W., Morgan D., Polchinski J.: Quantiation of falsk vacuum bubbles: a hamiltonian treatment of gravitational tunneling. Phys. Rev. D 42, 4042 (1990)CrossRefADSMathSciNetGoogle Scholar

Copyright information

© The Author(s) 2009

Authors and Affiliations

  1. 1.Physics DepartmentUCSBSanta BarbaraUSA

Personalised recommendations